The Duke of York said it had become clear to him in recent days that his association with the late convicted sex offender had become a “major distraction” to the royal family’s work.
The prince said he regrets his association with Epstein and “deeply sympathises” with his victims.
The Queen gave him permission to “step back from public duties for the foreseeable future”, Andrew said in a statement.
He also said he was “willing to help any appropriate law enforcement agency with their investigations, if required” over the Epstein probe.
Andrew has been heavily criticised for his performance in the TV interview on Saturday, in which he failed to express concern for Epstein’s victims.
He appeared to show no remorse for his close association with the convicted sex offender, who had abused many underage girls.
Pressure has been mounting in the days since the interview, with firms including BT and Barclays among a number of multimillion-pound businesses, universities and charities which have distanced themselves from Andrew.
In his statement, issued by Buckingham Palace, he said: “It has become clear to me over the last few days that the circumstances relating to my former association with Jeffrey Epstein has become a major disruption to my family’s work and the valuable work going on in the many organisations and charities that I am proud to support.
“Therefore, I have asked Her Majesty if I may step back from public duties for the foreseeable future, and she has given her permission.”
The duke added: “I continue to unequivocally regret my ill-judged association with Jeffrey Epstein. His suicide has left many unanswered questions, particularly for his victims, and I deeply sympathise with everyone who has been affected and wants some form of closure.
“I can only hope that, in time, they will be able to rebuild their lives.
“Of course, I am willing to help any appropriate law enforcement agency with their investigations, if required.”
In the Newsnight interview, the duke denied claims he slept with Virginia Giuffre, one of Epstein’s victims, on three separate occasions – twice while she was underage.
He said the alleged encounter in 2001 did not happen as he spent the day with his daughter, Princess Beatrice, taking her to Pizza Express in Woking for a party.
Ms Giuffre said the same alleged sexual liaison began with the duke sweating heavily as they danced at London nightclub Tramp.
But the duke said he had a medical condition at the time which meant he did not sweat. He said he had no recollection of meeting Ms Giuffre.
When asked by the BBC’s Emily Maitlis if he regretted the “whole friendship with Epstein”, the duke replied: “Now, still not and the reason being is that the people that I met and the opportunities that I was given to learn either by him or because of him were actually very useful.”
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